Clifford-valued NNs in Pattern Classification in .NET

Make Quick Response Code in .NET Clifford-valued NNs in Pattern Classification
Clifford-valued NNs in Pattern Classification
QR Code barcode library with .net
Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in Visual Studio .NET applications.
0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0 5 10 15 20 25 30 35 40
QR Code JIS X 0510 drawer on .net
using .net framework toembed qr code 2d barcode with asp.net web,windows application
0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0 5 10 15 20 25 30 35 40
.net Vs 2010 qr code jis x 0510 recognizerin .net
Using Barcode scanner for .NET Control to read, scan read, scan image in .NET applications.
0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0 5 10 15 20 25 30 35 40
Bar Code scanner in .net
Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.
0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0 5 10 15 20 25 30 35 40
Bar Code encoding in .net
use .net vs 2010 barcode development toembed barcode for .net
Figure 21.8 Curves of the quaternionic moments of (a) a rectangle; (b) a square; (c) a triangle; and (d) a circle.
Control qr code size with visual c#
to draw qr bidimensional barcode and qr code data, size, image with c# barcode sdk
9. Experimental Analysis
Aspx.cs Page qr code jis x 0510 writerwith .net
using barcode creation for asp.net web forms control to generate, create qr barcode image in asp.net web forms applications.
This section presents tests and applications of the Clifford MLP and SMVM. We explore the use of Gaussian kernels, kernels generated via automorphisms and one example of an SMVM which uses clustering hyperspheres as preprocessing. In order to show the effectiveness of Clifford moments as a preprocessing method, we consider a case of 2D shape classification.
Control qr code size on visual basic
to draw qrcode and quick response code data, size, image with visual basic barcode sdk
9.1 Test of the Clifford valued MLP for the XOR Problem
Render barcode in .net
using visual .net toaccess bar code on asp.net web,windows application
In this section, the geometric MLPs were trained using the generalized gradient descendent. The power of using bivectors for learning was confirmed with the test using the XOR function. Figure 21.9(a) shows that the quaternion-valued geometric nets GMLP0 2 0 and GMLP2 0 0 have a faster convergence rate than either the MLP or the P-QMLP the quaternionic multilayer perceptron of Pearson [15], which uses the activation function given by Equation (21.23). Figure 21.9(a) shows the MLP with two-and four-dimensional input vectors. An epoch means one training set comprised of four training pars. Since the MLP(4), working also in 4D, cannot outperform the GMLPs, it can be claimed that the better performance of the geometric neural network is due not
Barcode Code39 barcode library with .net
generate, create code 39 full ascii none in .net projects
Experimental Analysis
Code 128B drawer in .net
using barcode encoder for .net framework control to generate, create code 128c image in .net framework applications.
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
CBC barcode library in .net
use .net framework crystal royalmail4scc encoder torender british royal mail 4-state customer code for .net
XOR Problem
Control datamatrix data on .net c#
to incoporate data matrix barcode and gs1 datamatrix barcode data, size, image with .net c# barcode sdk
0.7 0.6 0.5 0.4 0.3 0.2 0.1
XOR Problem
QR Code ISO/IEC18004 implement for c#.net
using barcode writer for .net control to generate, create qr codes image in .net applications.
Error
Control upc a size on excel spreadsheets
to render upca and upc-a data, size, image with office excel barcode sdk
Error 0 100 200 300 400 500 600 700 800 900 1000 Epochs GMLP2,0 MLP(4) GMLP0,2 QMLP MLP(2)
Control upc a data with visual basic.net
to paint upc symbol and upc a data, size, image with vb barcode sdk
0.15 0.2 0.25 0.3 Normalized CPU time
Generate data matrix barcode for visual basic.net
using asp.net aspx crystal toinclude barcode data matrix on asp.net web,windows application
GMLP
Control pdf-417 2d barcode image on word documents
using word todraw pdf417 2d barcode with asp.net web,windows application
MLP(2)
UPC Code encoding for c#
using barcode generator for .net windows forms crystal control to generate, create upc-a supplement 2 image in .net windows forms crystal applications.
MLP(4)
Figure 21.9 (a) Learning XOR using the 2-input MLP denoted in the figure as MLP(2), 4-input MLP, denoted as MLP(4), quaternion-valued geometric nets GMLP0 2 0 and GMLP2 0 0 and P-QMLP; (b) comparison of the geometric neural network GMLP0 2 0 , the 2-input MLP, denoted MLP(2), and the 4-input MLP, denoted MLP(4).
to the higher dimensional quaternionic inputs, but rather to the algebraic advantages of the geometric neurons of the net. Figure 21.9(b) shows the error curves referring to the involved normalized computational time. The demanding computer resources of the MLP with four-dimensional input vectors (MLP(4)) is almost similar to the geometric neural network, however, its performance is lower than the geometric network. The learning performance of the MLP with two inputs (MLP(2)) is still not as good as that of the geometric neural net GMLP0 2 0 . The reader should see that the learning of geometric neural nets is improved due to the Clifford product computed in a higher dimensional space. It is worth noting in Figure 21.9(b) that the MLP(4), even working in a four dimensional space, cannot perform better than the geometric neural net.
9.2 Classification of 2D Patterns in Real Images
Now we will show an application of Clifford moments and geometric MLP using real images of the objects presented in Figure 21.10. The binarized images used to generate the moments
Figure 21.10 Images of the real objects.
Clifford-valued NNs in Pattern Classification
Cl21 Cl31 are depicted in Figure 21.11. The resulting curves of the Clifford moments are presented in Figure 21.12. Using binarized views of the objects unseen before by the neural network, we test the geometric MLP. The results in Table 21.1 show that the procedure performs well.
Figure 21.11 Binarized images of the objects.
0.5 0.5 0.4 0.3 0.2 0.1 0 0.4 0.3 0.2 0.1 0
0.1 0.2 0.3 0.4 0.5
0 10 20 30 40 50 60 70 80 90 100
0.1 0.2 0.3 0.4 0.5
0 10 20 30 40 50 60 70 80 90 100
0.5 0.4 0.3 0.2 0.1 0
0.1 0.2 0.3 0.4 0.5
0 10 20 30 40 50 60 70 80 90 100
Figure 21.12 Curves of the quaternionic moments of (a) a cylinder; (b) a cube and (c) a truncated pyramid.